Pure nanocrystalline metals generally lack structural stability due to the energy associated with their high volume fraction of grain boundaries, often exhibiting grain growth even at room temperature. However, the addition of solute atoms can stabilize the nanostructure against grain growth. The mechanism for this improvement in stability has been proposed to involve the reduction of grain boundary energy through the segregation of solute atoms to the grain boundaries, with possible secondary kinetic contributions based on solute drag. Accordingly, alloying has emerged as a critical component for the development and deployment of nanocrystalline materials, although our basic understanding of stability in nanocrystalline alloys remains incomplete.
A number of models pertaining to grain boundary segregation in nanocrystalline systems have been developed. Starting from the Gibbs adsorption equation, Weissmuller noted that the segregation of solute atoms to the grain boundaries in a dilute system reduces the grain boundary energy, γ:γ=γ0−Γ(ΔHseg+kT log [X])  (1)where the reduction in grain boundary energy from the unalloyed condition, γ0, is a function of the heat of segregation for the binary system (ΔHseg) and the solute excess (Γ) at the grain boundary for a particular global solute concentration (X) and temperature (T), with k the Boltzmann constant.
While the grain size-solute content relationships it predicted were promising with respect to experimental evidence, the stability of nanocrystalline systems was evaluated only with respect to changes in grain size. In fact, all of the analytical models to date suffer this deficiency. Suppression of grain growth is an important criterion for stabilizing a nanostructured alloy, but a potentially equally important stability is that with respect to phase separation. Even if a nanocrystalline alloy with grain boundary segregation is relatively more stable than a coarse-grained alloy of the same composition, the nanocrystalline state may never be achievable if the system phase separates.